A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics

Shea-Blymyer, Colin; Roy, Subhradeep; Jantzen, Benjamin C.

doi:10.3390/e23091191

Cited by 3 publications

(3 citation statements)

References 84 publications

(114 reference statements)

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“…The third does leave us with a residual problem of the naturalness of kinds: how do we ascertain without already knowing all of the variables involved whether two things are sufficiently similar in their causal structure? This is one of the questions posed by [24] as an "epistemic" problem of natural kinds, and the "dynamical kinds" solution explored in [25][26][27] provides just the sort of test we're looking for.…”

Section: Natural Kinds and The Genesis Of Variablesmentioning

confidence: 99%

“…Additionally, there is a growing body of methods for effectively and efficiently determining whether two systems belong to the same dynamical kind without explicitly determining their dynamical symmetries [25][26][27]. The method I'll employ in the next section is a modification of one of these previously published approaches.…”

Section: Natural Kinds and The Genesis Of Variablesmentioning

confidence: 99%

“…But with one modest assumption about the phenomenon being studied, one does not have to do so-a single timeseries will suffice. Assuming that the dynamics of the system of interest is time-invariant-such that if a state is shifted in time, all future states will be in shifted in time but otherwise identical to the untransformed series-then, as described in [27], we can split a single time series in two, and use each half like a separate experiment. This process is demonstrated in Figure 2.…”

Section: Natural Kinds and The Genesis Of Variablesmentioning

confidence: 99%

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Scientific Variables

Jantzen

2021

Philosophies

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Despite their centrality to the scientific enterprise, both the nature of scientific variables and their relation to inductive inference remain obscure. I suggest that scientific variables should be viewed as equivalence classes of sets of physical states mapped to representations (often real numbers) in a structure preserving fashion, and argue that most scientific variables introduced to expand the degrees of freedom in terms of which we describe the world can be seen as products of an algorithmic inductive inference first identified by William W. Rozeboom. This inference algorithm depends upon a notion of natural kind previously left unexplicated. By appealing to dynamical kinds—equivalence classes of causal system characterized by the interventions which commute with their time evolution—to fill this gap, we attain a complete algorithm. I demonstrate the efficacy of this algorithm in a series of experiments involving the percolation of water through granular soils that result in the induction of three novel variables. Finally, I argue that variables obtained through this sort of inductive inference are guaranteed to satisfy a variety of norms that in turn suit them for use in further scientific inferences.

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Section: Natural Kinds and The Genesis Of Variablesmentioning

confidence: 99%

Section: Natural Kinds and The Genesis Of Variablesmentioning

confidence: 99%

Section: Natural Kinds and The Genesis Of Variablesmentioning

confidence: 99%

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Scientific Variables

Jantzen

2021

Philosophies

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Recovery of dynamical similarity from lossy representations of collective behavior of midge swarms

Aung,

Abaid,

Jantzen

2023

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Understanding emergent collective phenomena in biological systems is a complex challenge due to the high dimensionality of state variables and the inability to directly probe agent-based interaction rules. Therefore, if one wants to model a system for which the underpinnings of the collective process are unknown, common approaches such as using mathematical models to validate experimental data may be misguided. Even more so, if one lacks the ability to experimentally measure all the salient state variables that drive the collective phenomena, a modeling approach may not correctly capture the behavior. This problem motivates the need for model-free methods to characterize or classify observed behavior to glean biological insights for meaningful models. Furthermore, such methods must be robust to low dimensional or lossy data, which are often the only feasible measurements for large collectives. In this paper, we show that a model-free and unsupervised clustering of high dimensional swarming behavior in midges (Chironomus riparius), based on dynamical similarity, can be performed using only two-dimensional video data where the animals are not individually tracked. Moreover, the results of the classification are physically meaningful. This work demonstrates that low dimensional video data of collective motion experiments can be equivalently characterized, which has the potential for wide applications to data describing animal group motion acquired in both the laboratory and the field.

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Multicriteria Optimization of a Dynamic System by Methods of the Theories of Similarity and Criteria Importance

et al. 2021

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The problem of multicriteria optimization of a dynamic model is solved using the methods of the similarity theory and the criteria importance theory. The authors propose the original model of a positional system with two hydraulic actuators, synchronously moving a heavy object with a given accuracy. In order to reduce the number of optimizing parameters, the mathematical model of the system is presented in a dimensionless form. Three dimensionless optimization criteria that characterize the accuracy, size, and quality of the dynamic positioning process are considered. It is shown that the application of the criteria importance method significantly reduces the Pareto set (the set of the best solutions). This opens up the possibility of reducing many optimal solutions to one solution, which greatly facilitates the choice of parameters when designing a mechanical object.

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A General Metric for the Similarity of Both Stochastic and Deterministic System Dynamics

Cited by 3 publications

References 84 publications

Scientific Variables

Scientific Variables

Recovery of dynamical similarity from lossy representations of collective behavior of midge swarms

Multicriteria Optimization of a Dynamic System by Methods of the Theories of Similarity and Criteria Importance

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